Idk???

So me and my SO has been dating for 1 year and 6 months and we was great together only laughter when we are together. I have never felt so happy before but it's so hard to be that way when we work together and have to hide our relationship because before I got my position at work dating was prohibited and he has a ex that works there and other women wants him and all they do is talk bad about him and tell me a lot of negative things about him...his ex always calls him baby and tells me stories about them still being together and spending time with each other some are lies and some I just don't know but she only tells me those things. She doesn't know about us but she do (if that makes sense)...now all our conversations are about his ex and the co workers and I think I'm driving him crazy with it and it's driving our relationship down the hill. I was wondering is I should stop nagging him about hearsay if I don't see it.....please don't be rude.